Items tagged with primes


HI MaplePrimes,

Is the Goldbach Weak Conjecture proven?

Consider odd primes p, q, and r.  The question is, Is the sum p+q+r sufficient to reach all odd numbers greater than 9?

See -'s_weak_conjecture

I tried an example.





Hi everybody,

So today is 10-28-2016 and I explored Leyland Numbers for the first time, on Maple.  Please see my example file and let me know what your impression is.


I have included a .pdf file so that the caual internet observer can also be aware of this information.



Hi EveryOne!

In the answer of the question "How to find roót of polynomial in finite field and extension finite field ", @Carl Love helped me to find roots of polynimial in finite field and extension finite field (At URL OR

However, with matrix M: =< x^4+x^3+x^6+x^7+x, 1+x^2+x^4+x^5+x^6, 1+x+x^2+x^3, x^7+x^6+x^5+x^4;

                                   x^7+x^5+x^4+x^3, x^6+x^4+x^2+1, x^4+x^3+x^6+x^7+x^2+x+1, 1+x^2+x^3+x^4+x^5; 

                                   x^7+x^5+x^2, x^7+x^5+x^3+x^2+1, x^2+x+x^6, x^2+x^3+x^5;
                                   x^4+x^3+x^6+1, 1+x^2+x^3+x^4, x^6+x^5+x^4+x^3, x^7+x^3 >;

and GF(2^8)/f(x)=x^8 + x^7 +x^6 + x +1 (i.e ext1:= Z^8+Z^7+Z^6+Z+1), then program don't run!

Please help me! Thanks so much.


I am trying to understand how maple "isprime" algorithm works. But I can't find anywhere what special_primes means.



isprime := proc(n)
local btor, nr, p, r;
   1   if not type(n,'integer') then
   2     if type(n,('complex')('numeric')) then
   3       error "argument must be an integer"
   4       return 'isprime(n)'
         end if
       end if;
   5   if n < 2 then
   6     return false
       elif member(n,isprime:-special_primes) then
   7     return true
       elif igcd(2305567963945518424753102147331756070,n) <> 1 then
   8     return false
       elif n < 10201 then
   9     return true
       elif igcd(8496969489233418110532339909187349965926062586648932736611545426342203893270769390909069477309509137509786917118668028861499333825097682386722983737962963066757674131126736578936440788157186969893730633113066478620448624949257324022627395437363639038752608166758661255956834630697220447512298848222228550062683786342519960225996301315945644470064720696621750477244528915927867113,n) <> 1 then
  10     return false
       elif n < 1018081 then
  11     return true
  12     r := gmp_isprime(n);
  13     if not r or n <= 5000000000 then
  14       return r
         end if;
  15     nr := igcd(408410100000,n-1);
  16     nr := igcd(nr^5,n-1);
  17     r := iquo(n-1,nr);
  18     btor := modp(('power')(2,r),n);
  19     if cyclotest(n,btor,2,r) = false or irem(nr,3) = 0 and cyclotest(n,btor,3,r) = false or irem(nr,5) = 0 and cyclotest(n,btor,5,r) = false or irem(nr,7) = 0 and cyclotest(n,btor,7,r) = false then
  20       return false
         end if;
  21     if isqrt(n)^2 = n then
  22       return false
         end if;
  23     for p from 3 while numtheory:-jacobi(p^2-4,n) <> -1 do
  24       NULL
         end do;
  25     return evalb(TraceModQF(p,n+1,n) = [2, p])
       end if
end proc

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